Timeline for Mapping cylinders of fibrations
Current License: CC BY-SA 2.5
8 events
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| May 4, 2012 at 23:01 | comment | added | John Klein | @Jeff: a word of advice. The term "fibration" means different things to different people. It's clear that you meant Hurewicz fibration in the above. I doubt the result you are asking about is true in the Serr e fibration case. | |
| Sep 29, 2011 at 15:03 | comment | added | Sergey Melikhov | The preprint mentioned in my previous comment is at arxiv.org/abs/1106.3249 | |
| Dec 17, 2010 at 2:12 | comment | added | Jeff Strom | @Sergey: this sounds very interesting! I can wait for your paper to make it to the arXiv -- no rush for me. | |
| Dec 17, 2010 at 2:07 | comment | added | Sergey Melikhov | If $E$, $B$ are metrizable and $p$ is uniformly continuous, and you replace quotient topology by the topology of quotient uniformity everywhere, then your two mapping cylinders will be homeomorphic (and also metrizable). The preprint about this is not on the arxiv yet (delayed by other sections) but I can share it. In fact, the two mapping cylinders are uniformly homeomorphic. So is there a nice model category structure on metrizable uniform spaces and u.c. maps? Unfortunately, not all pushouts are metrizable, though all adjunction spaces are. I wonder if some trick can save pushouts. | |
| Dec 16, 2010 at 16:28 | history | edited | Jeff Strom | CC BY-SA 2.5 |
added 197 characters in body
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| Dec 15, 2010 at 18:01 | comment | added | Jeff Strom | Yes, this was what I was trying to say: $q$ is a fibration if $p$ is locally trivial, without any modification. | |
| Dec 15, 2010 at 17:35 | comment | added | Somnath Basu | If your fibration $p:E\to B$ had fibre $F$ then $q:M_p \to B$ has pointwise fibre $CF$, the cone on $F$. If $p$ is locally trivial then $q^{-1}(U)\cong U\times CF$. I don't see where the modification of the topology of $M_p$ comes in this case at least! | |
| Dec 15, 2010 at 14:46 | history | asked | Jeff Strom | CC BY-SA 2.5 |